Static stretching while the muscles are cold is a useless exercise. Increasing ROM of joints is all 'stretching' ought aim to do. A large body of evidence suggests more limber muscles are actually less efficient if running fast is a goal. However, joint ROM is always good and dynamic, non-ballistic stretching before effort is a worthy principle.
But to enhance joint ROM effectively, muscles, tendons and ligaments are best stretched while warm, and held for some time in a static position. The idea is soft tissue including muscles, tendons and ligaments are viscoelastic. This means they are biphasic - they exhibit either viscous or elastic properties depending on the length and depth of any attempt to deform (stretch) them.
Stretching a muscle in the elastic region is mostly useless for long-term changes. You have to push past the 'yield' point into the plastic region, which more or less means any changes are more permanent. This gives greater joint ROM as it produces long-term changes in ligaments especially. These are pretty much immune to any dynamic pre-workout stretching you may do.
Ask your physio before trying any of these techniques for yourself.